A bevel gear unit comprising a bevel gear (11), a ball bearing (B.sub.1) coaxially mounted on the shaft of the bevel gear (11) and in contact with the back surface (17) thereof, a double spacer including an inner race spacer (12) and an outer race spacer (13) and mounted on the shaft of the bevel gear (11) behind the ball bearing (B.sub.1), ball bearings (B.sub.2, B.sub.3) mounted on the shaft of the bevel gear (11) behind the double spacer, and a bearing nut (15) screwed onto a threaded portion of the shaft of the bevel gear (11) behind the ball bearings (B.sub.2, B.sub.3). The axial length (l.sub.1) of the inner race spacer (12) is made smaller than the axial length (l.sub.2) of the outer race spacer (13) by a preloading allowance (.delta.), and the outer race spacer (13) is provided with threaded holes (t.sub.1) in the rear surface (f.sub.1) thereof. When applied to a mechanism having a plurality of coaxial bevel gears, particularly, to a wrist mechanism for an industrial robot, the bevel gear unit facilitates the preloading of the bearings.